A senior BBC source told the Mirror: “This really is his last chance. We have drawn a line in the sand, he was left in no doubt this has to be game changer.

“He spoke with various bosses and they were furious, Jeremy had to make amends.”

In an unprecedented stern statement, a BBC spokesman said: “Jeremy Clarkson has set out the background to this regrettable episode.

“We have made it absolutely clear to him, the standards the BBC expects on air and off.

“We have left him in no doubt about how seriously we view this.”

Clarkson issued a video lasting one minute and 38 seconds to explain his actions.

Looking tired and sounding unusually sombre, Clarkson said: “Ordinarily I don’t respond to newspaper allegations but on this occasion I feel I must make an exception.

“A couple of years ago I recorded an item for Top Gear in which I quoted the rhyme “eeny meeny miny moe”.

"Now of course I was well aware that in the best known version of this rhyme there is a racist expression that I was extremely keen to avoid.

“The full rushes show that I did three takes.

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"In two I mumbled where the offensive word would normally occur and in the third I replaced it altogether with the word teacher.

Now when I viewed this footage several weeks later I realised that in one of the mumbled versions, if you listen very carefully with the sound turned right up, it did appear that I’d actually used the word I was trying to obscure.

“I was mortified by this. Horrified.

"It is a word I loathe and I did everything in my power to make sure that version did not appear in the programme that was transmitted.

“In fact I have here the note I sent at the time to the production office and it says: ‘I didn’t use the n-word here but I’ve just listened through my headphones and it sounds like I did. Is there another take that we could use?’

“Please be assured I did everything in my power to not use that word.”

He then ended the statement saying he was “begging for your forgiveness” and that “my efforts weren’t quite good enough”.

Earlier today, David Cameron distanced himself from Clarkson as Downing Street piled pressure on the BBC to act over the presenter’s N-word outburst.

The Prime Minister’s official spokesman said: “The usage of that word, that would be quite wrong.”

Asked if Mr Cameron would use it, the spokesman added: “Certainly not.”

And asked whether the BBC should act, the spokesman added: “If there are these types of reports and allegations I’m sure that is something that the BBC will look at.”

Clarkson was a member of the “Chipping Norton set” that the PM and his wife socialised with in his Oxfordshire seat.

Mr Cameron even dressed up as the Stig to deliver a 50th birthday video message to the Top Gear presenter.

The PM’s spokesman could not say when they last met.

Anger: The BBC has given the presenter a final warning (Photo: Splash)

Other MPs also weighed into the furore. Shadow Culture minister Helen Goodman said that the BBC must act quickly.

Ms Goodman said: “Racist language is never funny.

"It is urgent that the BBC establishes the facts because millions of people would be disgusted if their licence fee has gone to reward its use on film.”

And Steve Rotherham, a member of the Commons Culture, Media and Sport committee said that Mr Clarkson should be fired.

The Labour MP said: “If the allegations are founded and that he has used that kind of inappropriate language the BBC needs to take action.

“Obviously what they will have to do is examine the footage and see exactly what he has said.”

Mr Rotherham said that it was ultimately up to the BBC to decide what should happen to the presenter, not MPs.

But he added: “If he has said what he is alleged to have said he will have to go.”

Lawyers for the Indian-born actor Somi Guha, who appeared in The Bill and other television shows, made a formal complaint to the BBC Trust as calls for Clarkson to be sacked gathered pace.

Piers Morgan wrote on Twitter: “Ron Atkinson was fired by ITV for using the N-word.

"Don’t see how the BBC can avoid firing Jeremy Clarkson if he did the same.”

He also wrote: “Clarkson been fired yet?” before adding shortly afterwards: “So it’s OK because Clarkson only MUMBLES the N-word? Got it. Let’s see him mumble that rhyme to his ‘hero’ @didierdrogba then.”

Criticism: David Cameron (Photo: Getty)

The footage is from the third episode of Top Gear Series 19 and is understood to have been filmed at the show’s race track in Surrey.

At the start of the show, Clarkson is seen driving a Toyota GT86 and a Subaru BRZ as he struggles to decide on which car is the best.

He decides to use the rhyme in order to decide upon the Toyota.

Michelle Bowman, a digital audio expert who analysed the footage before the Mirror published the story, provided a report which included a word for word transcript of the clip.

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Discrimination lawyer Lawrence Davies said: “His conduct is unacceptable and he should be removed from his presenting role.

“He clearly said it but what happens next is yet to be seen. What I think is also damning is that the BBC changed the output.

"The footage which was aired was different from this unseen footage.

"To me that says the BBC watched it back and deemed what was said inappropriate.”

However, last night there was also support of Clarkson as his millions of fans around the world rallied around him.

Some questioned the word which was uttered, saying it sounded more like “teacher” or even the word “Nissan”.

Others said it was merely a harmless rhyme repeated thousands of times during Clarkson’s childhood days at schools across Britain.

One fan wrote: “This whole Jeremy Clarkson thing is being blown way out of proportion.

"He shouldn’t use the word but there is no ill intent.”

Another said: “Jeremy Clarkson is not in the wrong for using the word n****r it was not in an offensive context nor did it cause alarm or distress to anyone.”

The row comes days after Top Gear’s producer apologised for broadcasting a “light-hearted” joke by Clarkson that sparked a complaint of racism.

An episode of the show , filmed in Burma and Thailand and shown in March, featured a scene in which the presenters built a bridge over the River Kwai, and as an Asian man walked over it Clarkson said: “That is a proud moment, but there’s a slope on it.”